Phase-contrast magnetic resonance imaging (PCMRI) is a method of encoding the velocity of particles traveling along a gradient field into the phase of the magnetic spin.

The velocity is encoded by applying appropriately designed gradient lobes in the velocity encoding direction; bipolar gradient lobes are one example. The two lobes of the bipolar gradient are created so their areas are equal and opposite. This makes the zeroth moment, m0, of the gradient waveform equal to 0 after the bipolar lobes. Since m0=0, no phase is imparted to static spins. Spins moving along the bipolar gradient direction experience a phase shift due to the difference in their positions from the first and second lobes of the bipolar gradient. This phase shift is proportional by the gyromagnetic ratio to the first moment, m1, of the bipolar gradient.φv=v*γ*m1  (eq. 2)
Higher order motion such as acceleration, jerk, snap, crackle, and pop can be encoded using the higher order gradient moments m2, m3, m4, m5, and m6 respectively. In practice, the bipolar gradient waveform used for velocity encoding can be overlapped with other waveforms in the pulse sequence such as ramp ups, ramp downs, and refocusing waveforms. This reduces echo times, repetition times, and scan times. Velocity encoding will be used to describe the invention due to its common use in clinical applications, although the invention may be used to improve temporal resolution in any technique that uses multiple encodings to generate a time series of images.
PCMRI sequences used for velocity encoding are designed with the m1 used to encode the velocity into phase. The limitation placed on the velocity encoded phase is that it cannot exceed 360° without experiencing wrapping or aliasing in the image. When aliasing occurs, the same phase angle encodes for two or more velocity values. An aliased pixel value creates ambiguity on the true velocity as shown in FIG. 1.
PC sequences for velocity encoding typically require an aliasing velocity, VENC, to be input by the user. This value is used to set the m1 such that the phase will not wrap and velocities between −VENC and +VENC will not be aliased. The range of non-aliased velocities are zero centered, allowing equally for velocities in the positive and negative directions. The range can also be shifted to allow for only positive velocities or only negative velocities or an arbitrary range. For further discussion, the zero centered range with limits ±VENC will be used.v→φv(−180° to +180° range)  (eq. 3)
One of the practical issues that has to be dealt with in PC imaging is an unknown background phase in an image. This background phase comes from a variety of sources (e.g. B0 inhomogeneity, susceptibility differences, etc.) and varies across the image affecting the accuracy of the velocity measurement.
                              background          ⁢                                          ⁢          phase          ⁢                                          ⁢          from          ⁢                                          ⁢          static          ⁢                                          ⁢          tissue                =                              ϕ            static                    ⁢                                          ⁢                                          =                                    ϕ              s                        ⁡                          (                              360                ⁢                °                ⁢                                                                  ⁢                range                            )                                                          (                  eq          .                                          ⁢          4                )            
Because of the background phase on the image, PC requires an additional data separation step that is not required in standard data acquisition. To compensate for φs, two complete datasets are acquired with some combination of φs and φv at each pixel. From these data sets φs and Øv can be separated and an image of phase due to velocity can be reconstructed. Standard data acquisition is as shown in FIG. 2. PC data acquisition requires the additional data separation step shown in FIG. 3.
As shown in FIG. 3, variables av,1 and av,2 represent the weighting of the velocity into the measured phase in the data sets. When playing out the pulse sequence, av,1, and av,2 are set by the m1 of the appropriately designed velocity encoding gradients. These values have to be known so that the data may be separated later. The process can be analogized to the process of encoding a message which is to be sent. An encryption key is used by the sender to take the original message and convert it to the encrypted form. The key is later used by the receiver for decryption to yield the original message.
When each measured data set is reconstructed using the appropriate spatial encoding methods, each pixel of the phase image has phase that comes from three sources; velocity: (φv); static background tissue (φs); and noise (φv).φnoise=φn  (eq. 5)
Currently two velocity encoding/decoding methods are commonly used: 1-sided and 2-sided encoding. 1-sided encoding collects two data sets: a velocity encoded, Venc, and velocity compensated, V0. The V0 is assumed to be the first data set and the Venc is assumed to be the second data set. The order of the data can be switched. For the V0 data, all of the phase in the measured data comes from the static background tissue and noise. The bipolar gradients are played out so there is no phase due to velocity.φ0=φs+φn,0  (eq. 6)
An important point to note is the assumption that static background phase is assumed to be constant for the acquisition of both of the data sets. Noise varies between the data sets so it is denoted with a subscript on the acquisition in which it comes from.
For 1-sided encoding, the second acquisition is Venc data. For this acquisition the bipolar gradient is played out to so that a +VENC velocity multiplied by av,2 yields +180° of phase shift and a −VENC velocity multiplied by av,2 yields −180° of phase shift. The magnitude of av,2 is set to prevent aliasing due to wrapping of the phase.
                                          ϕ            enc                    =                                    ϕ              v                        +                          ϕ              s                        +                          ϕ                              n                ,                enc                                                    ⁢                                  ⁢                              a                          v              ,              2                                =                                    180              ⁢              °                        VENC                                              (                  eq          .                                          ⁢          7                )            
The mapping of phase to velocity for the encoded and compensated images are shown in FIG. 4.
Data separation is then performed by subtracting the velocity compensated data set from the velocity encoded data set to yield the phase due velocity. This subtraction cancels out the common phase due to static tissue while maintaining the velocity phase which is present in only the Venc data set.
                                                                                          ϕ                  enc                                -                                  ϕ                  0                                            =                            ⁢                                                (                                                            ϕ                      v                                        +                                          ϕ                      s                                        +                                          ϕ                                              n                        ,                        enc                                                                              )                                -                                  (                                                            ϕ                      s                                        +                                          ϕ                                              n                        ,                        0                                                                              )                                                                                                        =                            ⁢                                                ϕ                  v                                +                                  ϕ                                      n                    ,                    enc                                                  +                                  ϕ                                      n                    ,                    0                                                                                                          (                  eq          .                                          ⁢          8                )            
The data is then reconstructed into an image where pixel intensity is set by the phase which is proportional to velocity. For simplicity, the magnitude of the complex signal has been ignored and only the phase retained. Due to the complex nature of the signal, there are multiple ways to perform the subtraction used for data separation. The phase difference method and complex difference methods are further discussed in the Handbook of MRI Pulse Sequences by Matt A. Bernstein, Kevin F. King, and Xiaohong Joe Zhou Elsevier, Academic Press, 2004 which is hereby incorporated by reference.
The other method which has been used is 2-sided encoding. 2-sided encoding is commonly used on General Electric (GE) MRI systems while SIEMENS has typically utilized 1-sided encoding. In 2-sided encoding the two data sets acquired are V− (data set 1) and V+ (data set 2). Again the order is arbitrarily set, does not represent a required acquisition sequence, and can be changed. For the V− acquisition the bipolar gradient is played out to so that a +VENC velocity multiplied by av,1 yields −90° of phase shift and a −VENC velocity multiplied by av,1 yields +90° of phase shift. The smaller phase sensitivity to velocity used in the V− (and V+) encoding is to prevent aliasing in the data separation step and is shown later.
                                          ϕ            -                    =                                                    -                                  ϕ                  v                                            2                        +                          ϕ              s                        +                          ϕ                              n                ,                -                                                    ⁢                                  ⁢                              a                          v              ,              1                                =                                                    -                90                            ⁢              °                        VENC                                              (                  eq          .                                          ⁢          9                )            
The V+ acquisition is played out so the bipolar gradient so that a +VENC velocity multiplied by av,2 would yield −90° of phase shift and a −VENC velocity multiplied by av,2 would yield +90° of phase shift.
                                          ϕ            +                    =                                                    +                                  ϕ                  v                                            2                        +                          ϕ              2                        +                          ϕ                              n                ,                +                                                    ⁢                                  ⁢                              a                          v              ,              1                                =                                                    +                90                            ⁢              °                        VENC                                              (                  eq          .                                          ⁢          10                )            
Data separation is then preformed by subtracting the V− data set from the V+ data set in the same way as 1-sided encoding to yield the phase due velocity.
                                                                                          ϕ                  +                                -                                  ϕ                  -                                            =                            ⁢                                                (                                                                                    +                                                  ϕ                          v                                                                    2                                        +                                          ϕ                      s                                        +                                          ϕ                                              n                        ,                        +                                                                              )                                -                                  (                                                                                    -                                                  ϕ                          v                                                                    2                                        +                                          ϕ                      s                                        +                                          ϕ                                              n                        ,                        -                                                                              )                                                                                                        =                            ⁢                                                ϕ                  v                                +                                  ϕ                                      n                    ,                    +                                                  +                                  ϕ                                      n                    ,                    -                                                                                                          (                  eq          .                                          ⁢          11                )            The mapping of phase to velocity for the positive and negative images are shown in FIG. 5.
The need for reducing the sensitivity by half from the Venc to the V+/V− data sets comes from the subtraction of φ+ and φ−. Even though a higher sensitivity wouldn't cause wrapping of the velocity phase in each of the data set, it could cause wrapping in the difference between the images. Therefore the sensitivity for each of the acquisitions in 2-sided has to be half the sensitivity of 1-sided.
Thus, conventional PC-MRI utilizes either a pair of velocity-encoded and velocity-compensated datasets or a pair of equal and opposite polarity velocity-sensitized k-space datasets. In either case, phase-difference or complex-difference reconstruction is performed on each complex data pair to eliminate any residual non-zero phase variation due to effects other than velocity. Conventional PC-MR velocity mapping requires twice as much data as standard MRI scans. This requirement either degrades the temporal sampling rate by a factor of two, or doubles the acquisition time in order to maintain temporal resolution.
Cardiac echo-sharing has been utilized to improve the effective temporal resolution in segmented cine and phase-contrast imaging. In echo-sharing, portions of k-space are shared between adjacent images for both velocity-compensated and velocity-encoded lines. Therefore, partial k-space data is shared and reconstructed from two or more temporally adjacent k-space data pairs. Because image characteristics are dominated by the central portion of k-space, echo-sharing methods require the acquisition of an additional central line or segment of k-space for each pair of reconstructed frames. Otherwise, if the central lines of k-space were shared between frames, those frames would contain substantially the same information.
The present invention of Shared Velocity Encoding (SVE) reconstruction can be used to increase the effective temporal resolution of PC-MRI. In conventional PC-MRI reconstruction, the phase difference is calculated from consecutive pairs of (+ −) velocity encoded k-space lines. Thus, if the total number of acquired k-space lines is N, the resulting number of reconstructed phase-difference lines is N/2. In contrast, the SVE PC-MRI method of the present invention shares data between consecutive images. By doing so, N−1 phase-difference lines from alternate polarity pairs (+ −), (− +), (+ −), etc., can be constructed from the N acquired k-space lines. The result is that the effective temporal resolution is increased by a factor of 2.
SVE reconstruction provides for improved methods of MRI blood flow velocity mapping. Additionally, the very high temporal resolution data acquisition necessary for MRI pulse wave velocity (PWV) measurement—that is not exhibited by the traditional methods of PC-MR imaging—is enabled by SVE reconstruction. Conventional MRI flow quantification methods require the acquisition of additional reference data to account for errors in the signal phase. SVE reconstruction eliminates the temporal resolution penalty associated with the acquisition of this additional reference data. The SVE reconstruction method can be combined with a segmented EPI readout to achieve high temporal resolution real-time velocity mapping by minimizing sensitivities to respiratory and cardiac motions. More benefits and additional applications of SVE reconstruction will become apparent upon review of the figures and detailed description that follows.